adequate data automatically. Because, in daily
work, it may happen that bad data rest so much
beyond our expectations in raw materials. We,
therefore, should waste computing minutes by
means of a program without filtering routine in
it. The load upon copmuter may readily become
double or triple.
Moreover, at the present step, we confront the
case in which automatic filtering is almost impos-
sible,—really we found such a case especially when
the problem concerns to the relation between bad
data and the true deformation of a model. In our
present opinion, the analytical method must be
investigated deeply from the stand point of model
deformation, the aims of which we may attain only
by the analytical method itself.
2. Absolute Orientation.
2-1. Absolute orientation. Absolute orientation
is a transformation of coordinate axis, without
matter how one single model or one strip as a
whole be treated. In this case transformation
equation is, as was verified by Rosenfield."
x’ COS qp COS « COS @ Sin « - sino sing cosx« sin o sin « — cos o sin Q9 cos x| x
y | = | —cos @ sin « COS @ COS « — Sin w Sin sin x sin © cos x + cos w sing sin « || y (1)
. * |
z' sin @ —SIN ® COS @ COS 0 COS @ la
But, to obtain rotational matrix of equation (1)
directly from observation equations in general is
not possible, because in the case of flat terrain,
the height differences of control points vanish and
the determinant of above matrix becomes zero
(or at least small).
To avoid this difficulty, we can make the com-
putation procedure completely the same as the
ordinary mechanical method, i.e.
1. Determine the approximate scale factor M
by Helmert method using the measured machine
coordinates (x, y) and ground coordinates (X, Y)
of control points.
2. We rotate the model or strip only for «b
and ©, but not for x, then putting x—0, equation
(1) becomes
x'=x cos P+y sin © sin Q—z sin P cos (2-1)
ot? sin © (2-2)
z'=x sin %— y cos P sin ®+zcos cos (2-3)
!
y @ ycosQ
We assume ® and are small, and instead of
z', we use the value £. then the equation (2-3)
becomes
4 —x dy 04s (3)
3. To obtain the approximate value of «P and
Q from equation (3), we introduce the coefficients
4, b, c, d and e to express «^ and Q as a function
of x, respectively. (assuming in general that each
inclination of model or strip varies as a linear
function of x)
b=ax+b
Q=cx+d (4)
€ —constant
and apply the least square to the following equa-
1) Rosenfield, G. H.: ‘The problem of exterior orientation in
Sept, 1959.
tion which is the rewritten form of equation (3)
by equation (4), i.e.
—Az= 2 —2=(ax+b)x—(ex+d)y+e (5)
4. Putting in equation (2) the approximate
value of «P and O thus obtained by equation (5)
and (4) we obtain the transformed model-or
strip-coordinates (x’, y', 2^) by the rotation ®
and ©. If vertical deformation of model or strip
be negligible, a or/and c will be put zero in equa-
tions (4) and (5).
5. Repeat the computation from (1) to (4),
considering the new coordinates (x', y’, z^) as the
originally measured values, until M converges with
some required accuracy.
6. If bending of a strip in (x, y) plane occurs,
the conformal transformation of second order is
very useful, instead of Helmert method.
The conformal transformation equation? is
X—X,-F Ax —By4 C(x? — y?) —2Dxy
Y=Y+Bx+Ay+D(x*— y?) +2Cxy (6)
Final values of plane coordenates (X, Y) of any
point are obtainable by Helmert method or con-
formal transformmation of second order {equation
(6)} and elevation Z is from equation (5) as fol-
lows
ZL={(ax+b)x—(ex+d)y+e+z}M e»
where (x, y, z) are the final values of model-or
strip-coordinates after when succesive rotations
of the model or the strip have been executed by
computation.
2-2. Semi-analytical method.
We classified the analytical method in two
classes: semi-analytical and pure-analytical, as the
photogrametry," Photogrammetric Engineering,
2) Suggested by Y. Ozaki, member of Geographical Survey Institute of Japan. Not published.
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